The pressure at the bottom of a liquid tank is not proportional to the

Water os flowing with speed of 10 m/s through a pipe with cross-sectional area of 8 cm². The water slowly descends 10 m. The pipe cross-sectional area at lower level increases to 16 cm^2. The pressure at the upper level  and lower level  is 1.0 x 10⁵ N/m² and ⍺ x 10⁵ N/m² respectively. The value of  constant ⍺ will be (Assume the density of water = 1000 kg/m³)

There is a hole in the bottom of  tank having water. If total pressure at bottom is 3 atm (1 atm = 10⁵ N/m²) then the velocity of water flowing from hole is

Molecules on the surface of the liquid have

A liquid drop having surface energy ‘E’ is spread into 512 droplets of same size. The final surface energy of the droplets is

Clouds float in air due to

A small metal ball of mass ‘m’ is dropped in a liquid contained in a vessel , attains a terminal velocity ‘v’. If a metal ball of same liquid then the terminal velocity will be

The angular velocity of a particle rotating in a circular orbit 100 times per minute is

Two solid cylinders P and Q of the same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of the mass concentrated near its surface , while Q has most of its mass neat its surface, while Q has most of its mass concentrated near the axis. What statement (s) is/(are) correct?

A mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

An electric fan has blades of length 30cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m. , the acceleration of a point on the tip of the blade is about

A string breaks under a load of 4 kg. A mass weighting 200 g is attached to the end of this string which is one metre long and rotated horizontally. The angular velocity of rotation when the string breaks, is nearly (g = 10m/s2)

A student weighting 667 N rides a steadily rotating Ferris wheel (student sits upright). At the highest point, the magnitude of the normal force N vector , if the wheel’s speed is doubled, is

A bend in level road has a radius of 100 m. The maximum speed with which a car turning this bend without skidding, if coefficient of friction between the tyres and the surface of the road is 0.8, will be (g=9.8 m/s2)

A aircraft executes a horizontal loop with a speed of 150 m/s with its wings banked at an angle of 12º. The radius of the loop is ( g=10 m/s2 ) 

Calculate the angular momentum of the earth due to rotation about its own axis. Assume that the earth is a sphere of mass 6 ✕ 10⌃24 kg and radius 6400km.

A swimmer while jumping into water from a height easily forms a loop in air, if

A uniform horizontal circular platform of mass 200kg is rotating in 10 r.p.m. about a vertical axis passing through its centre. A boy of mass 500 Kg is standing on its edge. If the boy moves to the centre of the platform, then the frequency of rotation would be

A body of mass 100 g is revolving in a horizontal circle. It its frequency of rotation is 3.5 r.p.s and radius of circular path is 0.5m, the angular speed of the body is

The angular separation between the minute hand and the hour hand of a clock at 12:20 pm is

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same mass M and radius R. They all spin with the same angular speed ⍵ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation.

A thin circular plate of mass M and radius R has its density varing as ⍴(r) = ⍴o r with ⍴o as constant and r is the distance from its center. The moment of Inertia of the circular plane about an axis perpendicular to the plate and passing through its edge is I = aMR⌃2. The value of the coefficient a is :